Acceleration of Free Fall

Investigate how the time to fall depends on the drop height, and use it to find the acceleration of free fall. Drag the metre rule sideways to line it up with the ball or card before you take a reading.

Results

h / m	t₁ / s	t₂ / s	t₃ / s	mean t / s	t² / s²

Results

s / m	L / m	Δt₁ / s	Δt₂ / s	Δt₃ / s	mean Δt / s	v / (m s⁻¹)	v² / (m² s⁻²)

Guided Investigation

Your aim is to find a value for the acceleration of free fall, g, using each method, and then to judge how much you trust each value. Treat this as an investigation: you are finding out whether the two methods agree and how good each one really is — not confirming an answer you already expect.

Part A — Explore first

Before you record anything, use both methods a few times.

On Method 1, release the ball from several different heights. Watch closely what happens in the moment between pressing release and the ball actually leaving the magnet.
On Method 2, drop the card from several different distances above the gate, and watch how the reading changes as you do.

Get a feel for how each apparatus behaves before you start measuring.

Part B — Method 1: timing a falling ball

Planning.

Decide what you will change, what you will measure, and what you will keep the same. How many times will you release the ball at each height before moving on, and what will you do with those repeated readings? Why is repeating worthwhile here?

Turning your readings into a straight line.

A graph of height against time is a curve, which is hard to read a value from. Which equation of motion links the distance fallen from rest to the time taken? Write it down, then rearrange it into the form (one quantity) = gradient × (another quantity). What will you put on each axis to get a straight line?

Finding g.

Plot your graph and draw a best-fit line by eye. Work out its gradient, including units. Using your rearranged equation, what is the link between this gradient and g? Calculate your value of g.

Does your line pass through the origin?

If the timer measured only the time the ball spends falling, where would you expect your best-fit line to cross the axes? Look at where it actually crosses. Now go back to the apparatus and release the ball once more, watching the ball and the timer together at the instant you press release. What do you notice? How could this explain what the intercept of your graph is telling you — and would it make your measured times too large or too small?

Part C — Method 2: speed through a light gate

Planning.

Decide what you will change, what you will measure, and what you will keep the same, and how you will use repeated readings.

From time to speed.

The datalogger gives you the time the card takes to pass through the gate. Using that time and the length of the card, how do you work out a speed? Now think carefully about what that speed really describes: is it the card’s speed at the exact instant it reaches the gate, or something else? What is happening to the card’s speed during the short time it is breaking the beam?

Turning your readings into a straight line.

Which equation of motion links the speed gained to the distance fallen from rest? Rearrange it into a straight-line form. What will you plot on each axis?

Finding g and reading the intercept.

Plot your graph, draw a best-fit line, and find its gradient with units. How is the gradient linked to g? Calculate g. Does your line pass through the origin? If the speed you calculated were exactly the speed at the gate, where should the line cross? Using your earlier answer about what the speed really describes, can you suggest why the line might cross above the origin instead?

Part D — Comparing the two methods

You now have a value of g from each method.

Do they agree?

Compare them with each other and with the accepted value. Are the differences small enough to be put down to random scatter in your readings, or is something more going on?

Both of your best-fit lines missed the origin, but for different reasons.

In one sentence each, say what caused the intercept in each method.

The harder question.

For each method, decide whether its error affects mainly the intercept of the graph (shifting the line up or down) or also the gradient (changing how steep the line is). The gradient is what gives you g, so an error that changes the gradient matters more for your value of g than one that only moves the intercept. On that basis, which of your two values of g do you trust more, and why?

For each method, suggest one change.

Suggest one change to the apparatus or the procedure that would reduce its main source of error.